Fighting was heaviest Thursday in Baiji, north of Baghdad, where militants have been battling government forces for about a week over control of an oil refinery, analysts said.

Iraqi officials said Thursday that government forces repelled the militants and retained control there, but analysts and one private contractor with ties to the Iraqi oil industry told NBC News it is not clear who controls the Baiji refinery.

According to Iraq analysts, the following cities are under the complete or partial control of ISIS and other militant groups: Mosul (the north's biggest city), Tikrit, Rawa, Tal Afar and Fallujah.

Some of the cities under government control have also witnessed fighting, including Ramadi, Saadiyah and Jalawla.

President Barack Obama said Thursday that the United States is prepared to take “targeted and precise” military action against Islamist militants in Iraq, but he pledged that American forces “will not be returning to combat.”